The present invention relates generally to methods utilized to calibrate sensors and, in an embodiment described herein, more particularly provides a method for calibrating pressure and temperature transducers utilized in tools in subterranean wells.
It is common practice to use transducers in downhole tools for various purposes. For example, in a drill stem test or other well test, important information regarding the present and future productivity of a well may be determined by evaluating pressure, temperature, flow rate, etc. data recorded during the test. Unfortunately, the accuracy of that information is necessarily dependent upon the accuracy of the recorded data from which it is derived.
Typically, the pressure, temperature, flow rate, etc. data is acquired from outputs of transducers or other sensor apparatus positioned downhole during the test. In this manner, the sensors are positioned in relatively close proximity to a particular formation or zone being evaluated in the test, thereby minimizing the contribution of wellbore storage effects, resistance to flow, temperature changes, etc. to the collected data. However, such downhole positioning of the sensors creates other problems which affect the accuracy of the sensor outputs.
Quartz piezoelectric pressure transducers are generally used in well tests, due to their superior accuracy as compared to other types of commercially available pressure transducers. When a conventional quartz pressure transducer is positioned downhole, however, it is subjected to whatever static or dynamic temperature conditions exist in the downhole environment. Since the output of a conventional quartz pressure transducer is affected by the temperature of the piezoelectric sensor therein, the precise manner in which the transducer output is affected by temperature must be known, and the output of the transducer must be appropriately corrected for the temperature at which the output data was taken, in order to increase the accuracy of the data.
In a similar manner, quartz piezoelectric temperature transducers may be affected by pressure applied thereto. Thus, if a quartz temperature transducer is subjected to pressures existing downhole during a well test, the accuracy of the acquired temperature data is affected. Fortunately, such inaccuracies in the temperature data are generally considered to be relatively minor, and so the temperature data is commonly used to correct the pressure data acquired by the pressure transducer. Nevertheless, it may be seen that the inaccuracies are compounded by using inaccurate temperature data to correct inaccurate pressure data.
Again, in a similar manner, flow rate data collected from the output of a flow rate sensor is typically affected by conditions existing downhole. For example, since the output of a common flow rate sensor is typically influenced by the temperature of the fluid for which the flow rate is being sensed, the flow rate sensor output data must be corrected for the temperature of the fluid at the time the output is generated. Such influence of fluid temperature on flow rate sensor output usually affects the accuracy of the acquired data greatest when the fluid is a gas, or a liquid with gas entrained therein.
Sensors used in downhole environments may be affected by other factors as well. For example, the output of a quartz piezoelectric pressure sensor is not only affected by the temperature of the surrounding environment, it is also affected by changes in the temperature of the surrounding environment, such as the rate of temperature change. This is due to the fact that the pressure sensor is sensitive to stresses in a quartz crystal thereof and stresses are induced in the quartz crystal in response to changes in the temperature of the crystal.
In the past, a quartz pressure transducer was statically calibrated by placing the transducer in a fluid bath at a known constant temperature and recording the output of the transducer at various pressures applied thereto. In this manner, a sensor output profile at that temperature was obtained. This procedure was then repeated at different temperatures, with a sensor output profile being generated for each temperature. Thus, a set of sensor output profiles was generated, each profile corresponding to a different temperature.
When the output of a particular pressure transducer was evaluated in actual practice, for example, after a well test, the output would be corrected based on the temperature of the surrounding environment at the time the output data was acquired. However, since the temperature of the surrounding environment typically fell between two of the temperatures used in the procedure to generate the sensor output profiles, it was generally necessary to interpolate between the corresponding sensor output profiles. Such interpolation usually assumed that a linear relationship existed between the output profiles and the corresponding temperatures at which they were generated and, since this linear relationship is generally not the case, this introduced further inaccuracies into the resulting corrected output data. Additionally, this method did not compensate at all for changes in temperature at the time the sensor output data was acquired.
Therefore, from the foregoing, it is apparent that a need exists for improved methods of calibrating sensors and, in particular, a need exists for utilizing such improved methods for calibrating sensors used in downhole environments. Furthermore, it would be desirable to provide such methods which compensate for changes in the environments in which the sensors are operated.
In carrying out the principles of the present invention, in accordance with described embodiments thereof, methods are provided which enable sensors to be calibrated with enhanced accuracy. The methods may be particularly useful for sensors utilized in applications where environmental conditions change during use of the sensors, such as in downhole transducer applications. Associated apparatus are also provided.
In one aspect of the present invention, a subject sensor which generates an output indicative of a stimulus is subjected to multiple levels of the stimulus. For example, a pressure sensor may be subjected to multiple fluid pressure levels. The output of the subject sensor is determined at each of the stimulus levels. A known accurate reference sensor is also subjected to the multiple stimulus levels and its output determined at each of the stimulus levels. The output of the subject sensor for the applied stimulus levels is then input to a neural network. The neural network is trained so that, when an output of the subject sensor is input to the neural network, the neural network simulates an output of the reference sensor.
In this manner, an output of the known accurate reference sensor is simulated in response to an input to the neural network of an output of the subject sensor. This method may be particularly useful in applications where the subject sensor is exposed only to changes in the stimulus level, or where the output of the subject sensor is not influenced by other stimulus levels. For example, where the subject sensor is a pressure sensor either not exposed to, or unaffected by, changes in temperature.
In another aspect of the present invention, the neural network has input to it multiple levels of a second stimulus which affects the output of the subject sensor. For example, where the subject sensor is a pressure sensor, the output of which is influenced by the temperature of the sensor. During training of the neural network, known levels of the second stimulus, such as in the form of output of a second known accurate reference sensor, at each of the outputs of the subject sensor are input to the neural network. Thereafter, the calibrated neural network output will compensate for the influence of the second stimulus level in simulating an output of the known accurate reference sensor in response to an input to the neural network of an output of the subject sensor and the second stimulus level.
In still another aspect of the present invention, a method of calibrating a subject sensor is provided in which outputs of both the subject sensor and a second sensor are input to a neural network. In this case, the subject sensor generates an output indicative of a first stimulus and the second sensor generates an output indicative of a second stimulus. The output of the subject sensor in response to each of multiple levels of the first stimulus is determined, with the subject sensor also being subjected to one of multiple levels of the second stimulus at each of the first stimulus levels. The output of the second sensor is determined in response to the level of the second stimulus at each of the first stimulus levels. A first known accurate reference sensor is also subjected to the first stimulus levels and its output determined at each of these. A second known accurate reference sensor is also subjected to the second stimulus levels and its output determined at each of these. The subject sensor outputs and the second sensor outputs are then input to a neural network and, using this data, the neural network is trained to simulate outputs of the reference sensors in response to input to the neural network of outputs of the subject and second sensors.
In this manner, an output of the first reference sensor is simulated in response to input to the neural network of outputs of the subject and second sensors. This method may be particularly useful in applications in which the subject sensor output is influenced by the stimulus indicated by the second sensor. For example, in applications where the subject sensor is a pressure sensor whose output is influenced by temperature, which property is indicated by the second sensor.
In yet another aspect of the present invention, a method of calibrating a subject sensor is provided in which the subject sensor generates an output indicative of a first stimulus, but the output is influenced at least transiently by a rate of change of a second stimulus. A second sensor is utilized in the method, the sensor generating an output indicative of the second stimulus. The subject and second sensors are subjected to known levels of the first and second stimuli at known discrete time intervals, and the outputs of the sensors at these stimulus levels are recorded. The subject and second sensor outputs, and the time intervals are then input to a neural network and the neural network is trained to generate an output which is a known mathematical function of the first stimulus in response to input to the neural network of outputs of the subject and second sensors at associated time intervals.
In this manner, a subject sensor, which has an output indicative of a first stimulus, but influenced at least in part by changes in a second stimulus, may be calibrated using a second sensor which has an output indicative of the second stimulus, with the outputs of the subject and second sensors being taken at known time intervals. This method may, for example, be useful where the subject sensor is a pressure sensor whose output is influenced by a rate of change in temperature of the surrounding environment.
These and other features, advantages, benefits and objects of the present invention will become apparent to one of ordinary skill in the art upon careful consideration of the detailed description of representative embodiments of the invention hereinbelow and the accompanying drawings.